000849786 001__ 849786 000849786 005__ 20230310131402.0 000849786 0247_ $$2doi$$a10.1007/s00791-018-0298-x 000849786 0247_ $$2ISSN$$a1432-9360 000849786 0247_ $$2ISSN$$a1433-0369 000849786 0247_ $$2Handle$$a2128/19505 000849786 0247_ $$2WOS$$aWOS:000439461000002 000849786 037__ $$aFZJ-2018-03898 000849786 041__ $$aEnglish 000849786 082__ $$a570 000849786 1001_ $$0P:(DE-Juel1)132268$$aSpeck, Robert$$b0$$eCorresponding author 000849786 245__ $$aParallelizing spectral deferred corrections across the method 000849786 260__ $$aBerlin$$bSpringer$$c2018 000849786 3367_ $$2DRIVER$$aarticle 000849786 3367_ $$2DataCite$$aOutput Types/Journal article 000849786 3367_ $$0PUB:(DE-HGF)16$$2PUB:(DE-HGF)$$aJournal Article$$bjournal$$mjournal$$s1532009866_1166 000849786 3367_ $$2BibTeX$$aARTICLE 000849786 3367_ $$2ORCID$$aJOURNAL_ARTICLE 000849786 3367_ $$00$$2EndNote$$aJournal Article 000849786 500__ $$aOnline first 000849786 520__ $$aIn this paper we present two strategies to enable “parallelization across the method” for spectral deferred corrections (SDC). Using standard low-order time-stepping methods in an iterative fashion, SDC can be seen as preconditioned Picard iteration for the collocation problem. Typically, a serial Gauß–Seidel-like preconditioner is used, computing updates for each collocation node one by one. The goal of this paper is to show how this process can be parallelized, so that all collocation nodes are updated simultaneously. The first strategy aims at finding parallel preconditioners for the Picard iteration and we test three choices using four different test problems. For the second strategy we diagonalize the quadrature matrix of the collocation problem directly. In order to integrate non-linear problems we employ simplified and inexact Newton methods. Here, we estimate the speed of convergence depending on the time-step size and verify our results using a non-linear diffusion problem. 000849786 536__ $$0G:(DE-HGF)POF3-511$$a511 - Computational Science and Mathematical Methods (POF3-511)$$cPOF3-511$$fPOF III$$x0 000849786 536__ $$0G:(GEPRIS)450829162$$aDFG project 450829162 - Raum-Zeit-parallele Simulation multimodale Energiesystemen (450829162)$$c450829162$$x1 000849786 588__ $$aDataset connected to CrossRef 000849786 773__ $$0PERI:(DE-600)1458972-2$$a10.1007/s00791-018-0298-x$$n3-4$$p75-83$$tComputing and visualization in science$$v19$$x1433-0369$$y2018 000849786 8564_ $$uhttps://juser.fz-juelich.de/record/849786/files/Paper.pdf$$yPublished on 2018-07-02. Available in OpenAccess from 2019-07-02. 000849786 8564_ $$uhttps://juser.fz-juelich.de/record/849786/files/Paper.gif?subformat=icon$$xicon$$yPublished on 2018-07-02. 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